The existing research of vibration synchronization among multiple rotors is mainly concentrated on plane vibration system. In this paper, the synchronization mechanism of the spatial vibration system actuated with tri-motor rotating in identical direction is studied. Firstly, the dynamic model is established, and the motion differential equations are deduced via Lagrange formulation. Then, small parameter average method is applied to explore the synchronization condition; Lyapunov equation and Routh-Hurwitz criterion are introduced to analyze the synchronization stability. Finally, the influence of the system parameter on synchronization is discussed by numerical calculation, and the electromechanical coupling simulation based on Matlab/Simulink is given to confirm the reliability of the theoretical analysis. The research result indicates that the vibration synchronization is affected by the horizontal distance between two coaxial motors, the installation height and the masses of three eccentric rotors (ERs), but the influence of the horizontal distance between coaxial motor and non-coaxial motor on synchronization is small.

现有的多转子间振动同步研究主要集中在平面振动系统上。本文研究了三电机同向旋转驱动的空间振动系统的同步机理。首先建立动力学模型，通过拉格朗日公式推导出运动微分方程。然后，应用小参数平均法探索同步条件；引入Lyapunov方程和Routh-Hurwitz判据来分析同步稳定性。最后通过数值计算讨论了系统参数对同步的影响，并给出了基于Matlab/Simulink的机电耦合仿真，验证了理论分析的可靠性。